#2020 年国赛- 填空题 阶乘约数
#约数定理：对于一个大于 1 的正整数N，如果它可以分解质因数为，N=p1^a1 * p2^a2... * pn^an，
#那么N的约数的个数就是(a1+1)*(a2+1)*(a3+1)*...*(an+1)。
def prime_factors(n):  #分解质因数
    factors = {}
    while n % 2 == 0:
        factors[2] = factors.get(2, 0) + 1
        n = n // 2
    i = 3
    while i * i <= n:
        while n % i == 0:
            factors[i] = factors.get(i, 0) + 1
            n = n // i
        i += 2
    if n > 2:
        factors[n] = 1
    return factors

factors_count = {}  # 记录每个质数的幂次数
for i in range(2, 101):
    factors = prime_factors(i)
    for p, exp in factors.items():
        factors_count[p] = factors_count.get(p, 0) + exp
# 运用约数定理
ans = 1
for j in factors_count.values():
    ans *= (j + 1)
print(ans)


